Constructive Solutions to the Riemann--Hilbert Problem and Middle Convolution

TL;DR

This paper introduces a general method using middle convolution to construct solutions to the Riemann--Hilbert problem, demonstrated on a specific Fuchsian system with four singular points.

Contribution

It provides a new constructive approach to solving the Riemann--Hilbert problem using middle convolution techniques.

Findings

Developed a scheme for constructive solutions to the Riemann--Hilbert problem.

Applied the method to a Fuchsian system with four singular points.

Illustrated the effectiveness of middle convolution in this context.

Abstract

In this paper we present a general scheme to generate constructive solutions to the Riemann--Hilbert problem via middle convolution and illustrate this approach for a Fuchsian system with four singular points.